Orange Order members parade through Belfast. Photograph: Peter Morrison/AP

Around 30,000 people have taken part in a march in Belfast to commemorate the 100th anniversary of the Ulster covenant, signed to oppose home rule for Ireland in 1912.

Thousands of spectators lined the streets to watch the event, while a cultural festival was being staged in the grounds of the Northern Ireland assembly at Stormont.

The six-mile march from central Belfast to Stormont is in memory of the covenant and in honour of Sir Edward Carson, the founding father of modern unionism.

While a feeder parade of more than 2,000 Orangemen and their bands from north Belfast passed off peacefully along the route, Catholic residents who live nearby accused loyalists of breaking a legal ruling that banned them from playing unionist anthems close to one of Belfast's oldest Catholic churches.

The Parades Commission – the body that adjudicates on controversial marches in Northern Ireland – ruled on Thursday that only religious hymns could be played while the procession went past St Patrick's chapel in Donegall Street.

The overwhelming majority of the bands that passed the church played a selection of hymns such as Abide With Me and Onward Christian Soldiers.

But Frank Dempsey, the chairman of the Carrick Hill Residents Association, claimed that at least one band played the loyalist anthem The Sash before they entered Belfast's major thoroughfare, Royal Avenue, a clear breach, the nationalists insisted, of the Parades Commission ruling.

"The determination was that only hymns were to be played down to Royal Avenue. That determination has been smashed. Some of the bands, yes, they did stick by the ruling – I have no problem with that – but a number of them broke it.

"Let's put it this way: it went over peacefully, but we are going to wait with bated breath, because when they [the unionists] get there and get a few liquors into them it might be a different story coming back," he said.

The Orangemen and bands from north Belfast are expected to pass Donegall Street by St Patrick's at around 6pm on Saturday evening. There is a massive security operation in place across parts of Belfast to ensure the unionists' return from the Stormont estate passes off peacefully. Hundreds of armoured police Land Rovers have been deployed along sectarian flashpoints across the city.

Speaking outside the church, the St Patrick's administrator Father Michael Sheehan expressed relief that the morning parade had passed off relatively peacefully.

Gerry Kelly, a Sinn Féin minister in the power-sharing government, observed the parade and praised the "dignity" of the protesters and also welcomed the fact that no violence had erupted along the route.

The Sinn Féin North Belfast assembly member called for dialogue between the residents, the Orange Order and others in the loyalist community to prevent the area around St Patrick's become yet another permanent sectarian flashpoint in the parading disputes.

The head of the Grand Orange Lodge of Ireland, Edward Stevenson, used the event to warn of the new threat to the unity of the UK from Alex Salmond's drive towards Scottish independence.

"We are delighted to welcome members of the loyal orders from England and Scotland. They too have demonstrated their loyalty to the crown and our Scottish brethren have publicly opposed any suggestion of independence for their country.

"We are all very clear about our long-term vision and that is to stay within the United Kingdom," he said.

Another senior Orangeman used the event to accuse the IRA and the Roman Catholic church of setting out to destroy the state of Northern Ireland.

The deputy grand master of the Orange Order in Ireland, the Rev Alastair Smyth, said the Westminster parliament had "rejected biblical values" and "encouraged homosexual activities with civil partnership legislation and the pressure is currently on to legalise same-sex marriage".